问题描述
我如何从一个十进制数转换为IEEE 754浮点数重新presentation这个例子
I have this example on how to convert from a base 10 number to IEEE 754 float representation
Number: 45.25 (base 10) = 101101.01 (base 2) Sign: 0
Normalized form N = 1.0110101 * 2^5
Exponent esp = 5 E = 5 + 127 = 132 (base 10) = 10000100 (base 2)
IEEE 754: 0 10000100 01101010000000000000000
这对我来说很有意义，除了一个通道：
This makes sense to me except one passage:
45.25 (base 10) = 101101.01 (base 2)
45是二进制101101那没关系..但他们是怎么获得0.25 .01？
45 is 101101 in binary and that's okay.. but how did they obtain the 0.25 as .01 ?
推荐答案
可以部分小数点后通过由新碱反复乘以转换为另一种碱（在这种情况下，新碱是2），这样的：
You can convert the part after the decimal point to another base by repeatedly multiplying by the new base (in this case the new base is 2), like this:
0.25 * 2 = 0.5
- >第一个二进制数字是0（取整数部分，即小数点前面的部分）
-> The first binary digit is 0 (take the integral part, i.e. the part before the decimal point).
继续小数点后部分乘以：
Continue multiplying with the part after the decimal point:
0.5 * 2 = 1.0
- >第二个二进制位为1（再次，采取不可分割的一部分）
-> The second binary digit is 1 (again, take the integral part).
这也是我们停止，因为小数点之后的部分，现在是零，所以没有什么更多的繁殖。
This is also where we stop because the part after the decimal point is now zero, so there is nothing more to multiply.
因此小数部分的最终二进制重新presentation为：0.01
Therefore the final binary representation of the fractional part is: 0.01.
编辑：
也可能是值得注意的是，这是相当频繁的二进制重新presentation是无限与有限的小数部分在基地启动10例甚至当：转换0.2 为二进制：
Might also be worth noting that it's quite often that the binary representation is infinite even when starting with a finite fractional part in base 10. Example: converting 0.2 to binary:
0.2 * 2 = 0.4 -> 0
0.4 * 2 = 0.8 -> 0
0.8 * 2 = 1.6 -> 1
0.6 * 2 = 1.2 -> 1
0.2 * 2 = ...
因此，我们结束了。0.001100110011 ...
使用这个方法，你看很容易，如果二进制重新presentation最终被无限的。
Using this method you see quite easily if the binary representation ends up being infinite.
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